Accessing the new rotation caused by "Track To" constraint
ObjectMatrixWorld.to_euler()

Proof using the console:

&gt;&gt;&gt; C.active_object.matrix_world.to_euler()
Euler((1.5707963705062866, -0.0, 0.0), 'XYZ')
&gt;&gt;&gt; import math
&gt;&gt;&gt; math.degrees(1.5707963705062866)
90.00000250447813



Further reading: Incorrect matrix_world after transformation 
API link: https://docs.blender.org/api/current/mathutils.html#mathutils.Matrix
Custom panel example: https://blender.stackexchange.com/a/66941/31447